Protesters Joe Hiller (l.) Milton Cornejo (c.), and Maru Mola sit chained together, blocking the road in front of the federal Northwest Detention Center in the Tacoma Tideflats, on Feb 24, 2014. Organizers with the Not One More Deportation campaign say they want to draw attention to deportations that break up families.

President Obama has ordered a review of his administration’s deportation policies with the goal of making them more “humane,” following accusations by advocates for immigrants that US practices are lacking in compassion.

In a meeting with the Congressional Hispanic Caucus (CHC) leadership Thursday evening, Mr. Obama said he is asking the Department of Homeland Security to address enforcement practices that the advocates say target not just high-priority criminals and recent illegal immigrants but also undocumented immigrants who have built lives in the US.

The announcement fired up Obama's GOP critics, who said that the administration can't be trusted to enforce the nation's immigration laws.

Obama asked Secretary of Homeland Security Jeh Johnson to review the department’s current practices to see "how it can conduct enforcement more humanely within the confines of the law," according to a White House statement.

Obama, whose administration to date has deported almost 2 million foreigners in the country illegally, has been under boiling pressure from the Hispanic caucus and pro-immigration activists nationwide to recalibrate how the federal government enforces its immigration laws.

Such critics have alleged that the administration’s practices lack compassion – going after immigrants who have committed no other crime except entering the US – and result in families splintered between border fences.

That criticism has become all the more visible in recent months, as advocates turn to more extreme measures to press Obama to intervene in what they say is a problem that can’t wait for a gridlocked Congress to stop politicking.

Moreover, the criticism of Obama has also become personal. The CHC Immigration Task Force chairman, Luis Gutierrez (D) of Illinois, who was at the meeting with the president Thursday, had last week called Obama a “deporter-in-chief” and a “dishonest” president, chiding him for unfulfilled campaign promises to overhaul immigration policies, according to Roll Call.

But, in a statement after the meeting, Mr. Gutierrez took a different tone, pinning the holdup not on Obama but on Congress.

“It is clear that the pleas from the community got through to the president,” he said. “The president clearly expressed the heartbreak he feels because of the devastating effect that deportations have on families.”

“I agree with the president that the ultimate solution and responsibility for fixing our broken immigration system rests with the Republican majority in the House of Representatives and we will work together to demand Republicans take action,” he added.

In that statement, Gutierrez appeared to cede to the Obama administration’s longtime stance that the administration, bound by current federal laws that require it to meet quotas for detaining undocumented immigrants, can’t fix the deportation issue on its own.

Indeed, Obama and his top officials have for years responded to calls for the administration to right deportation wrongs with aggressive executive action by saying that the Oval Office is doing all that it can on the issue, but, so long as the Hill stonewalls legislation on the issue, cannot do more.

Still, Obama in 2012 ordered deportation reprieves for undocumented immigrants brought to the US as young children. Plus, an August directive from the Immigration and Customs Enforcement office ordered agents not to arrest undocumented immigrants who are primary caregivers of minor children, and it has issued similar directives ordering leniency for longtime residents and students, among others.

Federal government data for the fiscal year 2013 – which, for the first time, broke down deportation numbers into deportations handled along the US border and deportation processed in the US interior – also suggests that most deportations come from the border, not from inside the US, where settled families might be split up, their lives upended.

But the White House has not had much luck winning congressional go-ahead for an overhaul of the nation's immigration laws. In June, a bipartisan bill to retool the US’s immigration laws passed the Senate. But it has been hung up in the Republican-controlled House, where GOP lawmakers bristled at its reforms, saying that the US-Mexican border is not well enough policed as it is and that immigration policies should be sterner, not laxer.

GOP House members in January offered a set of principles supporting legislation that prioritizes a “zero tolerance policy” for people either trying to enter or living in the US without legal papers. Such a policy would be a precursor to providing paths to citizenship to undocumented immigrants, according to the principles.

The House also on Wednesday passed a bill that would give either chamber of Congress the power to sue the White House for failure to enforce federal laws.

On Friday, GOP lawmakers said that Obama’s review of immigration reforms could signal just that kind of executive overstep.The Obama administration has already opted to defer action on deportation of the children of illegal immigrants, without congressional authorization, they said.

“This latest action further demonstrates that the administration cannot be trusted to enforce any immigration plan from Congress,” said Sen. Jeff Sessions (R) of Alabama, in a statement.

On the other hand, some advocates for an immigration overhaul said that they expected more from the executive office than a review alone and that Obama’s announcement did not go far enough. Pablo Alvarado, director of the National Day Labor Organizing Network, said in a statement after the Thursday meeting that the president had “no excuse” for not following through on pledges to fix immigration policies that break up families.